Solve sqrt{14^2-(5sqrt{3})^2}

$$\sqrt { 14 ^ { 2 } - ( 5 \sqrt { 3 } ) ^ { 2 } }$$

Evaluate

$$11$$

Solution Steps

Calculate 14 to the power of 2 and get 196.

$$\sqrt{196-\left(5\sqrt{3}\right)^{2}}$$

Expand \left(5\sqrt{3}\right)^{2}.

$$\sqrt{196-5^{2}\left(\sqrt{3}\right)^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\sqrt{196-25\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\sqrt{196-25\times 3}$$

Multiply 25 and 3 to get 75.

$$\sqrt{196-75}$$

Subtract 75 from 196 to get 121.

$$\sqrt{121}$$

Calculate the square root of 121 and get 11.

$$11$$

Factor

$$11$$